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On the primitivity of group algebras of certain classes of soluble groups of finite rank
Sbornik. Mathematics, Tome 186 (1995) no. 3, pp. 447-463 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper it is proved in detail that the group algebra $kG$ of a finitely generated metabelian group $G$ of finite rank over a field $k$ of characteristic zero is primitive if and only if its $FC$-centre $\Delta(G)$ is trivial. 
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     title = {On the primitivity of group algebras of certain classes of soluble groups of finite rank},
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     volume = {186},
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     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_3_a8/}
}
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A. V. Tushev. On the primitivity of group algebras of certain classes of soluble groups of finite rank. Sbornik. Mathematics, Tome 186 (1995) no. 3, pp. 447-463. http://geodesic.mathdoc.fr/item/SM_1995_186_3_a8/

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